Risks and Associations in Statistical Analysis
Absolute, Relative and Attributable Risks
Outcomes or differences that we are interested in:
Differences in means or proportions
Odds ratio (OR) – association of
two
variables
Relative Risk (RR) – association of
two
variables
Correlation coefficient – association of
two
variables
Outcomes or differences that we are interested in:
Differences in means or proportions
Odds ratio (OR) – association of
two
variables
Relative Risk (RR) – association of
two
variables
Correlation coefficient – association of
two
variables
Quantitative
Correlation coefficient
Qualitative
Chi square (χ2) test
Odds ratio, relative risk
Quantitative
Correlation coefficient
Qualitative
Chi square (χ2) test
Odds ratio, relative risk
Linearity and Direction are two concepts we
are interested in
Positive Linear Relationship
Negative Linear Relationship
Weak or Non-Linear Relationship
Correlation coefficient is the measure of direction
and strength of associations!
A nurse wanted to be able to predict the
laboratory HbA1c result (a
measure of blood
glucose control) from the fasting blood glucoses
which
she measured in her clinic. On 12
consecutive diabetic patients she noted
the
fasting glucose and simultaneously drew blood
for HbA1c.
An occupational therapist developed a scale for measuring
physical
activity and wondered how much it correlated to
Body Mass Index (BMI)
in 12 of her adult patients.
Cross Table
is u
sed to
calculate association
of t
wo
qualitative
variables
If first variable has
r
categories, second
variable
c
categories, then we have an
r
×
c
cross table
.
Cross Table – associations of YPEL5 genotypes
with
disease X
Cross Table is input for calculation of: risks, relative risk (RR),
odds ratio (OR)
Risk is the probability that an event
will happen.
Risk of geting a disease in the exposure group: a/(a+b)
Risk of geting a disease in the non-exposure group: c/(c+d)
People at risk
If one in every 100 patients suffers a side-
effect from
a treatment, the risk is
1⁄100 = 0.01=1%
C
alculated by dividing the
risk in the
treated
or exposed group
by the risk in the
control or
non-
exposed group
.
RR=1 -
no difference in risk
between the groups
RR>1 - the rate of the
event is increased
compared to
controls.
RR
<1
-
the rate of th
e
event is reduced
compared to
controls.
Always check for 95% CI of RR!!!
I
f
95%
CI for a risk ratio
does not include
1
(no
difference in risk),
it is statistically significant
.
RR=1 -
no difference in risk
between the groups
RR>1 - the rate of the
event is increased
compared to
controls.
RR
<1
-
the rate of th
e
event is reduced
compared to
controls.
A cohort of 1000 regular football players and 1000 non-footballers
were
followed to see if playing football was significant in the
injuries that they
received.
After 1 year of follow-up there had
been 12 broken legs in the football
players and only four in the
non-footballers.
The risk of a footballer breaking a leg was therefore 12/1000 or 0.012.
The 95% CI was calculated to be 0.97 to 9.41.
The
risk of a non-footballer breaking a leg was 4/1000 or 0.004.
The risk ratio of breaking a leg was therefore 0.012/0.004 which equals
3
As the CI
includes the
value 1
we
cannot exclude the possibility that
there was no difference in
the risk
of footballers and non-footballers
breaking a leg. However, given
these results
further investigation
would clearly be warranted
.
U
sed in “cohort studies”
◦
studies that follow a group (cohort) over a period of
time and
investigate the effect of a treatment or
risk
factor.
Used by epidemiologists in studies looking
for factors
which do harm
It
is a way of comparing patients
who already
have a certain condition (cases) with
patients
who do not (controls) – a “case–control
study”.
For
rare events
its value approximates that of
the
relative risk
(RR)
C
alculated by dividing the
number of times an
event happens by the number of
times it does not
happen.
Odds of
cases being exposed
: a/c
Odds of
controls being exposed
: b/d
One boy is born for every two births, so the
odds of
giving birth to a boy are
1:1 (or
50:50) = 1⁄1 = 1
If one in every 100 patients suffers a side-
effect from
a treatment, the odds are
1:99 =
1⁄99 = 0.0101
C
alculated by dividing the odds of having
been exposed to a risk factor by
the odds in
the control group.
OR=1 -
no difference in risk
between the groups
(odds are same)
OR>1 - the rate of the
event is increased
in patients
who have
been exposed
to the risk factor.
OR
<1
-
the rate of th
e
event is reduced
Always check for 95% CI of
O
R!!!
I
f
95%
CI for a
odds
ratio
does not include
1
(no
difference in
odds
),
it is statistically significant
.
OR=1 -
no difference in risk
between the groups
(odds are same)
OR>1 - the rate of the
event is increased
in patients
who have
been exposed
to the risk factor.
OR
<1
-
the rate of th
e
event is reduced
O
R
=
a
d
/
b
c
=
2
.
2
9
Odds for cases (patients with cancer) being smokers
are 2.29 times greater than for controls
H
elpful in trying to work out how worthwhile
a
treatment is in clinical practice
.
ARR is the difference between the
event rate
in the
intervention group
and that in the
control group
.
NNT is the
number of patients who need to
be
treated for one to get benefit.
RRR is the
proportion by which the
intervention
reduces the event rate
.
ARR =
improvement rate in the intervention group
improvement rate in
the control group =
80% – 60% = 20%
NNT
=
1/ARR=1/0.2=5
Or if you use percentages!
NNT
=
100/ARR=100/20%=5
Fi
ve women have to be treated for one to get
benefit.
The incidence of candidiasis was reduced from 40%
with placebo to 20%
with treatment , i.e. by half.
RRR=
d
e
vid
e
the absolute risk reduction by the
control event rate
= 20%/40%=50%
Explore concepts like absolute, relative, and attributable risks, differences in means or proportions, odds ratio, relative risk, correlation coefficient, and more in statistical analysis scenarios involving laboratory results and physical activity measurement.
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Presentation Transcript
Outcomes or differences that we are interested in: Differences in means or proportions Odds ratio (OR) association of two variables Relative Risk (RR) association of two variables Correlation coefficient association of two variables
Outcomes or differences that we are interested in: Differences in means or proportions Odds ratio (OR) association of two variables Relative Risk (RR) association of two variables Correlation coefficient association of two variables
Quantitative Correlation coefficient Qualitative Chi square ( 2) test Odds ratio, relative risk
Quantitative Correlation coefficient Qualitative Chi square ( 2) test Odds ratio, relative risk
Linearity and Direction are two concepts we are interested in Positive Linear Relationship Negative Linear Relationship Weak or Non-Linear Relationship
Correlation and Correlation coefficient and strength coefficient is of associations is the the measure measure of of direction direction strength of associations! !
A nurse wanted to be able to predict the laboratory HbA1c result (a measure of blood glucose control) from the fasting blood glucoses which she measured in her clinic. On 12 consecutive diabetic patients she noted the fasting glucose and simultaneously drew blood for HbA1c.
An occupational therapist developed a scale for measuring physical activity and wondered how much it correlated to Body Mass Index (BMI) in 12 of her adult patients.
Cross Table of two qualitative variables If first variable has r categories, second variable c categories, then we have an r c cross table. Cross Table is used to calculate association
Disease X YES NO TOTAL Genotype YPEL5 AA 2 0 2 AB 1 3 4 BB 0 4 4 TOTAL 3 7 10 Cross Table associations of YPEL5 genotypes with disease X
Cross Table is input for calculation of: risks, relative risk (RR), odds ratio (OR)
Risk is the probability that an event will happen. People at risk Risk of geting a disease in the exposure group: a/(a+b) Risk of geting a disease in the non-exposure group: c/(c+d)
If one in every 100 patients suffers a side- effect from a treatment, the risk is 1 100 = 0.01=1%
Calculated by dividing the risk in the treated or exposed group by the risk in the control or non-exposed group. R RR = exp osed R exp non osed RR=1 - no difference in risk between the groups RR>1 - the rate of the event is increased compared to controls. RR<1 - the rate of the event is reduced compared to controls.
Always check for 95% CI of RR!!! If 95% CI for a risk ratio does not include 1 1 (no difference in risk), it is statistically significant. RR=1 - no difference in risk between the groups RR>1 - the rate of the event is increased compared to controls. RR<1 - the rate of the event is reduced compared to controls.
A cohort of 1000 regular football players and 1000 non-footballers were followed to see if playing football was significant in the injuries that they received. After 1 year of follow-up there had been 12 broken legs in the football players and only four in the non-footballers. The risk of a footballer breaking a leg was therefore 12/1000 or 0.012. The risk of a non-footballer breaking a leg was 4/1000 or 0.004. The risk ratio of breaking a leg was therefore 0.012/0.004 which equals 3 The 95% CI was calculated to be 0.97 to 9.41. As the CI includes the value 1 we cannot exclude the possibility that there was no difference in the risk of footballers and non-footballers breaking a leg. However, given these results further investigation would clearly be warranted.
Used in cohort studies studies that follow a group (cohort) over a period of time and investigate the effect of a treatment or risk factor.
Used by epidemiologists in studies looking for factors which do harm It is a way of comparing patients who already have a certain condition (cases) with patients who do not (controls) a case control study . For rare events the relative risk (RR) rare events its value approximates that of
Calculated by dividing the number of times an event happens by the number of times it does not happen. Odds of cases being exposed: a/c Odds of controls being exposed: b/d
One boy is born for every two births, so the odds of giving birth to a boy are 1:1 (or 50:50) = 1 1 = 1 If one in every 100 patients suffers a side- effect from a treatment, the odds are 1:99 = 1 99 = 0.0101
Calculated by dividing the odds of having been exposed to a risk factor by the odds in the control group. a a d c = = OR b b c d OR=1 - no difference in risk between the groups (odds are same) OR>1 - the rate of the event is increased in patients who have been exposed to the risk factor. OR<1 - the rate of the event is reduced
Always check for 95% CI of OR!!! If 95% CI for a odds ratio does not include 1 1 (no difference in odds), it is statistically significant. OR=1 - no difference in risk between the groups (odds are same) OR>1 - the rate of the event is increased in patients who have been exposed to the risk factor. OR<1 - the rate of the event is reduced
cases controls smokers 156 (a) 221 (b) non-smokers 80 (c) 260 (d) OR = ad/bc = 2.29 Odds for cases (patients with cancer) being smokers are 2.29 times greater than for controls
Helpful in trying to work out how worthwhile a treatment is in clinical practice.
ARR is the difference between the event rate in the intervention group control group NNT is the number of patients who need to be intervention group and that in the control group. number of patients who need to be treated for one to get benefit. treated for one to get benefit. RRR is the proportion by which the intervention proportion by which the intervention reduces reduces the the event event rate rate.
ARR = improvement rate in the intervention group improvement rate in the control group = 80% 60% = 20%
NNT = 1/ARR=1/0.2=5 Or if you use percentages! NNT = 100/ARR=100/20%=5 Five women have to be treated for one to get benefit.
The incidence of candidiasis was reduced from 40% with placebo to 20% with treatment , i.e. by half. RRR=devide the absolute risk reduction by the control event rate= 20%/40%=50%
